ABC is a triangle with AB = AC. D is any point on

Question

ABC is a triangle with AB = AC. D is any point on the side BC. E and F are point on the side AB and AC, respectively; such that DE is parallel to AC, and DE is parallel to AB Prove thatDF + FA + AE + ED = AB + AC

Aditi Chauhan · Accepted Answer

Hello Student,
Please find the answer to your question Given that AB = AC &there4; &ang;1 = &ang;2 . . . . . . . . . . . . . . . . . . . . . . (1) But AB || DF (given ) and BC is transversal &there4; &ang;1 = &ang;3 . . . . . . . . . . . . . . . . . . . . . . . . . (2) From equation (1) and (2) &ang;2 = &ang;3 &rArr; DF = CF . . . . . . . . . . . . . . . . . . . . . . . (3) Similarly we can prove DE = BE Now, DF + FA + AE +ED = CF + FA + AE + BE = AC + AB [using equation (3) and (4)] ThanksAditi ChauhanaskIITians Faculty

Algebra> ABC is a triangle with AB = AC. D is any ...

ABC is a triangle with AB = AC. D is any point on the side BC. E and F are point on the side AB and AC, respectively; such that DE is parallel to AC, and DE is parallel to AB Prove that
DF + FA + AE + ED = AB + AC

Simran Bhatia , 11 Years ago

Aditi Chauhan

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Algebra> ABC is a triangle with AB = AC. D is any ...

ABC is a triangle with AB = AC. D is any point on the side BC. E and F are point on the side AB and AC, respectively; such that DE is parallel to AC, and DE is parallel to AB Prove thatDF + FA + AE + ED = AB + AC

Simran Bhatia , 11 Years ago

Aditi Chauhan

LIVE ONLINE CLASSES

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ABC is a triangle with AB = AC. D is any point on the side BC. E and F are point on the side AB and AC, respectively; such that DE is parallel to AC, and DE is parallel to AB Prove that
DF + FA + AE + ED = AB + AC